Question

In the following figure, three semicircles are given. If OA = OB = 2 cm. then the area of the whole figure =______ ${cm}^2.$

• A. 12$\pi$
• B. 8$\pi$
• C. 10$\pi$
• D. 3$\pi$

Answer 1

Answer: (A)

12$\pi$

We have: OA = OB = 2 cm = radius of larger semicircle = diameter of smaller semicirclesSo, OC = OD = 1 cm = radius of smaller semicirclesArea of the two small semicircles of radius 1 cm = 2(πr22) = π(1)2 = π cm2Area of the larger semicircle of radius 2 cm = πr22 = π(2)22 = 2π cm2So, total area = 2π + π = 3π cm2